This is in response to one of the questions posed in today's TOK class.
Which is the right answer:
Mathematics is the search for answers (with numbers/ of numbers/ by numbers).
I would argue that is is "by numbers" because the numbers only have meaning because we give them meaning. Mathematics, to me, seems to be a way for mankind to make abstract concepts like speed, predicting population growth, movement, etc. into concepts we can grasp. As a result the numbers help us quantify aspects of the world. The numbers allow us to make abstract concepts tangible and then understand their meaning. It is only by using numbers that we can think at a higher level.
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5 comments:
Stephanie- I agree with your choice of preposition.
It took me a while to choose for myself, but I had originally nixed "of numbers", simply because the "search for answers of numbers" relates to a solution to a numerical problem-but math does not have to be only numerical.
"with numbers" seems too simplistic a definition. For example, here is a possible question in a math book: Suppose you need five gallons of gas to get to grandma's house. You have four gallons in the car. Are you able to get to grandma's house?
Now, the answer to this question is "no". The answer is not "with numbers", because the answer "no" does not involve a number. But most people would agree that this question is a basic mathematical question.
I agree with both of your that "by numbers" best fits the definition of math. However, I disagree with the example that you used to refute the preposition "with". Isn't "five" gallons a number? Furthermore, to solve this problem, many other numbers are essential. For example, you would need the distance from where you are to grandma's house. While I agree that "with numbers" is too simplistic to serve as the sole definition, I cannot think of an example of math that is not solved with numbers. Maybe it would be best to include both "with" and "by"?
Mathematics, in general, involves using numbers to solve problems. In that sense, mathematics is the search for answers "with numbers." So, I agree with Elise that "with numbers" should be included as part of the definition, despite its simplicity.
I agree with the others that "by numbers" best fits the definition of mathematics, and that "of numbers" certainly does not best fit the definition. A quote from one of my readings this week, to me, exemplifies and validates this point quite well:
"Science [mathematics] is built up of facts [numbers], as a house is built up of stones; but an accumulation of facts [numbers] is no more a science [mathematics] than a heap of stones is a house." -- Reuben Abel, Man is the Measure, 85.
If math were defined as solely finding answers "with numbers," then it wouldn't really do that much for us. What's the point of knowing about derivatives, integrals, and sine functions if they can't be applied to real life, in order to find "real" answers? "Real" answers, in this circumstance, I define as "answers providing a better understanding of the world around us." If math did not help us find these "real" answers, then math wouldn't be that important, I don't think - like Stephanie said, numbers "help us quantify aspects of the world. The numbers allow us to make abstract concepts tangible and then understand their meaning." Numbers, whether one likes it or not, are products of the human mind, created in order to help us better explain the world. That is, essentially, the purpose of numbers.
Through them, we can find important answers regarding the world around us. This involves using the numbers - true - but it is through, or by, these numbers which we conduct our search for answers. This is the nature of mathematics. This is the reason that - in my opinion - "by numbers" best fits the definition of mathematics.
That said, which one is the "right" answer? They can all be right, in my opinion - it all depends on one's perception of what mathematics itself is.
To me, however, "by numbers" is the best fit. I don't want a heap of stones... I want a house.
Elise-I do agree with you that the process of my example does involve numbers. What I had meant to exemplify with the particular scenario created above is that the answer to the question, "can you reach the house" is a yes or no answer; the final answer does not involve a number, even though the process to answer the question does.
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